Correct, Chase has notes that the card is not available to you if you currently have any of the personal cards already on the application page. They make exception for the business cards. Currently each business card is counted separately so you could hold 3 SW cards at once as long as it's 1 personal (any flavor), 1 Biz Premier, and 1 Biz Performance.
Also, the card is not available if you've received a sign up bonus for any of the personal cards in the last 24 months. Since you said you had it for years I assume this isn't a problem for you.
For any one else curious, if you view the "Offer Details" link on the SW cards application it'll provide the criteria needed to get that card. For instance this is the language from the personal card offers:
The product is not available to either (i) current Cardmembers of any Southwest Rapid Rewards® Credit Card, or (ii) previous Cardmembers of any Southwest Rapid Rewards Credit Card who received a new Cardmember bonus within the last 24 months. This does not apply to Cardmembers of the Southwest Rapid Rewards Business Card and Employee Credit Card products.